Pertanyaan

Buktikan identitas trigonometri berikut. 2 cos 3 x − cos x sin x − 2 sin 3 x = tan x Gunakan identitas: cos 2 α = 1 − 2 sin 2 α = 2 cos 2 x − 1

Buktikan identitas trigonometri berikut.

$\frac{sin x - 2 sin ^{3} x}{2 cos ^{3} x - cos x} = tan x$

Gunakan identitas:

$cos 2 α = 1 - 2 sin^{2} α = 2 cos^{2} x - 1$

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style fraction numerator sin space x minus 2 space sin cubed space x over denominator 2 space cos cubed space x minus cos space x end fraction equals fraction numerator sin space x open parentheses 1 minus 2 space sin squared space x close parentheses over denominator cos space x open parentheses cos squared space x minus 1 close parentheses end fraction equals fraction numerator sin space x open parentheses cos space 2 x close parentheses over denominator cos space x open parentheses cos space 2 x close parentheses end fraction equals fraction numerator sin space x over denominator cos space x end fraction equals tan space x end style$